Architecture of planetary systems

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Planets and Astrobiology (2016-2017)G. Vladilo

Multiple planetary systems

•  The discovery of multiple planetary systems around stars other than the Sun allows us to investigate the general architecture of planetary systems

•  Open questions:–  How planets of different sizes and masses are located with respect

to the host star?Are giant planets typically closer or distant from the star?Which is the relative location and orbital periodicity of terrestrial planets in the systems ?Is there evidence for mean motion resonance?

–  Is the Solar System architecture representative of a large fraction of planetary systems or is it anomalous?

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Importance of the study of �multiple planetary systems

•  Multiple planetary systems provide tests of planetary formation–  Models of planetary formation are extremely complex and do not

provide unique solutions: the output of model simulations are very sensitive to even little variations of initial conditions

–  Given this situation, it is impossible to understand the general configuration of planetary systems by only using the properties of the Solar System

–  Having a large number of planetary systems allows us to study which is the probability of occurrence of a particular planetary configuration

–  In this way, the models of planetary formation are constrained to reproduce, from the statistical point of view, the observed distribution of planetary architectures

Observations of multiple planetary systems

•  All the methods of exoplanet observations are able, in principle, to detect multiple planetary systems

•  The first confirmed exoplanets, detected in 1992 with the pulsar timing technique, were actually part of a multiple planetary system (Wolszczan & Frail, 1992)

•  Given the large efficiency of the Doppler and transit methods, statistical properties of multiple planetary systems are based on data collected with such observational methods

•  As a test of the reliability of the detection of multiple planetary systems, a test of dynamical stability of the observed configuration is usually performed

Analysis of dynamical stability of multiple planetary systems

HD 183263 b,c (Wright et al. 2009)

•  This type of analysis requires integration of the orbits by means of numerical methods –  the goal is to test whether the

orbital parameters inferred from the observations correspond to a long-term stable physical configuration

–  this test can also be used to constrain the parameter space of the results, especially when the experimental error bars are large

–  among different types of numerical integrators, “symplectic integrators” are preferred

Symplectic integrators

•  In describing the motion of dynamical systems, a sequence of deterministic algebraic steps are executed from an initial to some final state

•  Such algebraic mappings include the classical fourth-order Runge-Kutta iteration for the approximate solution of ordinary differential equations (e.g. Press et al. 2007)

•  These conventional integrators carry the penalty of “numerical dissipation”, which results in a secular change of energy even in a conservative system–  Positional errors grow quadratically with time

•  Symplectic integrators do not suffer from these disadvantages, since they are built in such a way to preserve total energy and angular momentum of the N-body system–  The positional errors grow linearly with time

Statistics of planetary systems �discovered with the Doppler and transit methods

Multiple planetary systems discovered with the Doppler method�(Marcy et al. 2008)

•  Frequency

–  About 10-15% of all the exoplanet systems detected with the Doppler method happen to be multiple systems

–  The fraction of multiple systems discovered tends to increase with increasing accuracy of the observations and with increasing temporal baseline of the observations

–  The true fraction is expected to be higher, perhaps most planets being in multiple systems

semi-majoraxis

•  Architecture–  Planetary systems show a large

variety in their architecture–  Giant planets can be either close or

distant from the central star

Multiple planetary systems discovered with the Doppler method�

(Marcy et al. 2008)

•  Statistics of multiple planetary systems –  even if the statistics is still relatively small, some systematic differences

appear to be present between single planets and multiple systems –  as an example, the planet distribution as a function of semimajor axis

seems to be flatter for multiple systems than for single planets–  A peak of �hot jupiters� around a ~ 0.03-0.07 AU and of giant planets

beyond a ~ 1 AU are not seen in the statistics of multiple systems

Wright et al. (2009)

Wright et al. (2009)

•  Statistics of multiple planetary systems–  Apparently, the mechanisms that yield an accumulation of giant planets at

small and large semimajor axis are not working in multiple systems–  The differences suggest the existence of different mechanisms of planet

migration, still hard to understand given the low statistics and the presence of selection effects

–  Migration of giants from outer to inner regions might destroy multiplicity

•  Planetary systems with more than 4 planets discovered with Kepler (Lissauer et al. 2011)–  Large variety of planetary architectures–  In this sample, smaller planets tend to lie closer to the star than giant planets–  Selection effects of the transit method tend to favour detection of large

planets (rather than small planets) close to the star

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Multiple planetary systems: Kepler results

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Multiple planetary systems: Kepler results

•  Interpretation–  The migration of giant planets towards the central star could alter the orbital

inclinations of smaller planets; as result, the probability for them to be discovered with the transit method would become smaller

Multiple planetary systems: Kepler resultsThe statistics of exoplanets is dominated by relatively small planets

(smaller than Neptune)However, in multiple planetary systems the fraction of neptunian planets is

higher (86%) than in single systems (69%)Latham et al. (2011)

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Multiple planetary systems: Kepler results•  Possible interpretation-  The mass of protoplanetary disk that is not used to build up giant

planets is available to be incorporated in planets of lower mass

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Multiple planetary systems: Kepler results

•  Nearby planets tend to have similar radii –  Results inferred from the cumulative distribution of the ratio of the radii of

neighbouring planets –  In absence of migration mechanisms, this result suggests that the final size

of the planets at the epoch of their formation depends on the properties of the protoplanetery disk at a given distance from the star

–  The result is considered to be unaffected by selection bias

Rossiter-McLaughlin effect

Distorsion of the stellar absorption-line profiles induced by the transit of a planet in front of the stellar disk

Its detection requires both the transit and Doppler techniques

The same effect was discovered in stellar binaries by Rossiter and McLaughlin almost one century ago

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The Rossiter–McLaughlin (RM) effect

Line profile of the stellar photospheric

absorption

Effect on the stellar magnitude

Effect on the radial velocity

Gaudi & Winn (2007)

Produces an anomalous signal in the Keplerial radial velocity curve during the transit

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The Rossiter–McLaughlin (RM) effect

Covino et al. (2013)

days

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The Rossiter–McLaughlin (RM) effect

The radial velocity profile of the Rossiter-McLaughlin signal depends on the angle λ between the planetary orbit and the stellar equatorial plane of rotation

The Rossiter–McLaughlin (RM) effect

•  By modelling the radial velocity profile of the Rossiter-MacLaughlin signal, one can measure the angle λ between the rotation spin of the host star and the orbital spin of the transiting planet –  The direction of the star rotation spin is supposed to indicate the

original angular momentum of the protoplanetary accretion disk –  The planetary orbital spin may have changed as a result of

dynamical interactions among planetary system bodies

Measuring λ provides information on the dynamical processes that have taken place during planetary formation and evolution

This casts light on the possible origin of different types of planetary architectures observed at the present time

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The Rossiter–McLaughlin (RM) effect:�analysis of sample of �hot jupiters�

•  The obliquity of the spins, λ, tends to decrease with time

–  In the first stages after planetary formation, a significant fraction of �hot jupiters� show a high obliquity

–  These cases favour scenarios of planetary formation where the migration of Hot Jupiters has been driven by dynamical instabilities, rather than migration along the plane of the protoplanetary disk

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Albrecht et al. (2012)

The Rossiter–McLaughlin (RM) effect:�analysis of sample of �hot jupiters�

•  The obliquity tends to decrease at low effective temperature of the star, Teff

–  Interpretation: the outer layers of stars with low Teff are characterized by convection

–  Tidal interaction with the convective layers tends to align the rotation and orbital spins

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Albrecht et al. (2012)

5000 6000 7000 8000 Teff

The Rossiter–McLaughlin (RM) effect

•  Application to confirm candidate transit planets

–  Confirmation by means of the Doppler method of planet candidates discovered with the transit method is extremely time consuming (requires several orbital periods)

–  This observational effort can be dramatically reduced by observing the radial velocity signal only during the transit epoch

–  The detection of an anomalous radial-velocity signal with Rossiter-McLaughlin characteristics would provide an immediate confirmation of the planetary origin of the minimum of the light-curve

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Circumbinary planets•  Planets in binary/multiple stellar systems

–  A significant fraction of exoplanets have been found around binary or multiple stellar systems

–  In radial velocity surveys, most circumbinary planets are gas giants orbiting the main component (S-type orbits)

–  At small separations of the binary stars (� 100 AU) a smaller fraction of planets have been found

Open and filled circles: planets around single and binary stars, respectively

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Circumbinary planets

•  In the Kepler transit survey, a number of circumbinary planets in P-type orbits have been found–  Red and orange: primary and

secondary star–  Blue: planet orbit–  In the bottom right panel the

orbits are scaled to the critical semimajor axis for stability of P-type orbits, ac

–  The planets seem to lie just outside the critical value ac